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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 26 Mar 2012 03:52:40 -0400

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Mar/26/t1332748423w9rs4k3i6mo9swq.htm/, Retrieved Thu, 02 May 2024 03:27:18 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=164081, Retrieved Thu, 02 May 2024 03:27:18 +0000

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No (this computation is public)

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Estimated Impact

127

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-       [(Partial) Autocorrelation Function] [autocorelatie (di...] [2012-03-26 07:52:40] [e15deab13e19d5d27f52a3832c12141e] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164081&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164081&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164081&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.256175	-1.9677	0.026903
2	0.001837	0.0141	0.494395
3	-0.110343	-0.8476	0.200055
4	-0.148889	-1.1436	0.128697
5	0.042128	0.3236	0.373695
6	0.059118	0.4541	0.325714
7	-0.070512	-0.5416	0.295063
8	-0.000779	-0.006	0.497624
9	0.24484	1.8807	0.032479
10	-0.067721	-0.5202	0.302443
11	-0.037293	-0.2865	0.387768
12	-0.310973	-2.3886	0.010065
13	-0.062582	-0.4807	0.316253
14	-0.003676	-0.0282	0.488785
15	0.339641	2.6088	0.005747
16	-0.221421	-1.7008	0.047127
17	0.092293	0.7089	0.240585
18	0.054689	0.4201	0.337978

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.256175 & -1.9677 & 0.026903 \tabularnewline
2 & 0.001837 & 0.0141 & 0.494395 \tabularnewline
3 & -0.110343 & -0.8476 & 0.200055 \tabularnewline
4 & -0.148889 & -1.1436 & 0.128697 \tabularnewline
5 & 0.042128 & 0.3236 & 0.373695 \tabularnewline
6 & 0.059118 & 0.4541 & 0.325714 \tabularnewline
7 & -0.070512 & -0.5416 & 0.295063 \tabularnewline
8 & -0.000779 & -0.006 & 0.497624 \tabularnewline
9 & 0.24484 & 1.8807 & 0.032479 \tabularnewline
10 & -0.067721 & -0.5202 & 0.302443 \tabularnewline
11 & -0.037293 & -0.2865 & 0.387768 \tabularnewline
12 & -0.310973 & -2.3886 & 0.010065 \tabularnewline
13 & -0.062582 & -0.4807 & 0.316253 \tabularnewline
14 & -0.003676 & -0.0282 & 0.488785 \tabularnewline
15 & 0.339641 & 2.6088 & 0.005747 \tabularnewline
16 & -0.221421 & -1.7008 & 0.047127 \tabularnewline
17 & 0.092293 & 0.7089 & 0.240585 \tabularnewline
18 & 0.054689 & 0.4201 & 0.337978 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164081&T=1

[TABLE]
[ROW][C]Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]ACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]1[/C][C]-0.256175[/C][C]-1.9677[/C][C]0.026903[/C][/ROW]
[ROW][C]2[/C][C]0.001837[/C][C]0.0141[/C][C]0.494395[/C][/ROW]
[ROW][C]3[/C][C]-0.110343[/C][C]-0.8476[/C][C]0.200055[/C][/ROW]
[ROW][C]4[/C][C]-0.148889[/C][C]-1.1436[/C][C]0.128697[/C][/ROW]
[ROW][C]5[/C][C]0.042128[/C][C]0.3236[/C][C]0.373695[/C][/ROW]
[ROW][C]6[/C][C]0.059118[/C][C]0.4541[/C][C]0.325714[/C][/ROW]
[ROW][C]7[/C][C]-0.070512[/C][C]-0.5416[/C][C]0.295063[/C][/ROW]
[ROW][C]8[/C][C]-0.000779[/C][C]-0.006[/C][C]0.497624[/C][/ROW]
[ROW][C]9[/C][C]0.24484[/C][C]1.8807[/C][C]0.032479[/C][/ROW]
[ROW][C]10[/C][C]-0.067721[/C][C]-0.5202[/C][C]0.302443[/C][/ROW]
[ROW][C]11[/C][C]-0.037293[/C][C]-0.2865[/C][C]0.387768[/C][/ROW]
[ROW][C]12[/C][C]-0.310973[/C][C]-2.3886[/C][C]0.010065[/C][/ROW]
[ROW][C]13[/C][C]-0.062582[/C][C]-0.4807[/C][C]0.316253[/C][/ROW]
[ROW][C]14[/C][C]-0.003676[/C][C]-0.0282[/C][C]0.488785[/C][/ROW]
[ROW][C]15[/C][C]0.339641[/C][C]2.6088[/C][C]0.005747[/C][/ROW]
[ROW][C]16[/C][C]-0.221421[/C][C]-1.7008[/C][C]0.047127[/C][/ROW]
[ROW][C]17[/C][C]0.092293[/C][C]0.7089[/C][C]0.240585[/C][/ROW]
[ROW][C]18[/C][C]0.054689[/C][C]0.4201[/C][C]0.337978[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164081&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164081&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.256175	-1.9677	0.026903
2	0.001837	0.0141	0.494395
3	-0.110343	-0.8476	0.200055
4	-0.148889	-1.1436	0.128697
5	0.042128	0.3236	0.373695
6	0.059118	0.4541	0.325714
7	-0.070512	-0.5416	0.295063
8	-0.000779	-0.006	0.497624
9	0.24484	1.8807	0.032479
10	-0.067721	-0.5202	0.302443
11	-0.037293	-0.2865	0.387768
12	-0.310973	-2.3886	0.010065
13	-0.062582	-0.4807	0.316253
14	-0.003676	-0.0282	0.488785
15	0.339641	2.6088	0.005747
16	-0.221421	-1.7008	0.047127
17	0.092293	0.7089	0.240585
18	0.054689	0.4201	0.337978

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.256175	-1.9677	0.026903
2	-0.068269	-0.5244	0.300988
3	-0.13691	-1.0516	0.14863
4	-0.235589	-1.8096	0.037727
5	-0.091892	-0.7058	0.241534
6	0.004951	0.038	0.484897
7	-0.12169	-0.9347	0.176872
8	-0.107944	-0.8291	0.205185
9	0.250642	1.9252	0.029513
10	0.084705	0.6506	0.258904
11	-0.056979	-0.4377	0.331614
12	-0.339678	-2.6091	0.005742
13	-0.222522	-1.7092	0.046332
14	-0.225664	-1.7334	0.044128
15	0.169271	1.3002	0.099296
16	-0.257309	-1.9764	0.026393
17	-0.117958	-0.9061	0.184297
18	0.058703	0.4509	0.326854

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.256175 & -1.9677 & 0.026903 \tabularnewline
2 & -0.068269 & -0.5244 & 0.300988 \tabularnewline
3 & -0.13691 & -1.0516 & 0.14863 \tabularnewline
4 & -0.235589 & -1.8096 & 0.037727 \tabularnewline
5 & -0.091892 & -0.7058 & 0.241534 \tabularnewline
6 & 0.004951 & 0.038 & 0.484897 \tabularnewline
7 & -0.12169 & -0.9347 & 0.176872 \tabularnewline
8 & -0.107944 & -0.8291 & 0.205185 \tabularnewline
9 & 0.250642 & 1.9252 & 0.029513 \tabularnewline
10 & 0.084705 & 0.6506 & 0.258904 \tabularnewline
11 & -0.056979 & -0.4377 & 0.331614 \tabularnewline
12 & -0.339678 & -2.6091 & 0.005742 \tabularnewline
13 & -0.222522 & -1.7092 & 0.046332 \tabularnewline
14 & -0.225664 & -1.7334 & 0.044128 \tabularnewline
15 & 0.169271 & 1.3002 & 0.099296 \tabularnewline
16 & -0.257309 & -1.9764 & 0.026393 \tabularnewline
17 & -0.117958 & -0.9061 & 0.184297 \tabularnewline
18 & 0.058703 & 0.4509 & 0.326854 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164081&T=2

[TABLE]
[ROW][C]Partial Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]PACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]1[/C][C]-0.256175[/C][C]-1.9677[/C][C]0.026903[/C][/ROW]
[ROW][C]2[/C][C]-0.068269[/C][C]-0.5244[/C][C]0.300988[/C][/ROW]
[ROW][C]3[/C][C]-0.13691[/C][C]-1.0516[/C][C]0.14863[/C][/ROW]
[ROW][C]4[/C][C]-0.235589[/C][C]-1.8096[/C][C]0.037727[/C][/ROW]
[ROW][C]5[/C][C]-0.091892[/C][C]-0.7058[/C][C]0.241534[/C][/ROW]
[ROW][C]6[/C][C]0.004951[/C][C]0.038[/C][C]0.484897[/C][/ROW]
[ROW][C]7[/C][C]-0.12169[/C][C]-0.9347[/C][C]0.176872[/C][/ROW]
[ROW][C]8[/C][C]-0.107944[/C][C]-0.8291[/C][C]0.205185[/C][/ROW]
[ROW][C]9[/C][C]0.250642[/C][C]1.9252[/C][C]0.029513[/C][/ROW]
[ROW][C]10[/C][C]0.084705[/C][C]0.6506[/C][C]0.258904[/C][/ROW]
[ROW][C]11[/C][C]-0.056979[/C][C]-0.4377[/C][C]0.331614[/C][/ROW]
[ROW][C]12[/C][C]-0.339678[/C][C]-2.6091[/C][C]0.005742[/C][/ROW]
[ROW][C]13[/C][C]-0.222522[/C][C]-1.7092[/C][C]0.046332[/C][/ROW]
[ROW][C]14[/C][C]-0.225664[/C][C]-1.7334[/C][C]0.044128[/C][/ROW]
[ROW][C]15[/C][C]0.169271[/C][C]1.3002[/C][C]0.099296[/C][/ROW]
[ROW][C]16[/C][C]-0.257309[/C][C]-1.9764[/C][C]0.026393[/C][/ROW]
[ROW][C]17[/C][C]-0.117958[/C][C]-0.9061[/C][C]0.184297[/C][/ROW]
[ROW][C]18[/C][C]0.058703[/C][C]0.4509[/C][C]0.326854[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164081&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164081&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.256175	-1.9677	0.026903
2	-0.068269	-0.5244	0.300988
3	-0.13691	-1.0516	0.14863
4	-0.235589	-1.8096	0.037727
5	-0.091892	-0.7058	0.241534
6	0.004951	0.038	0.484897
7	-0.12169	-0.9347	0.176872
8	-0.107944	-0.8291	0.205185
9	0.250642	1.9252	0.029513
10	0.084705	0.6506	0.258904
11	-0.056979	-0.4377	0.331614
12	-0.339678	-2.6091	0.005742
13	-0.222522	-1.7092	0.046332
14	-0.225664	-1.7334	0.044128
15	0.169271	1.3002	0.099296
16	-0.257309	-1.9764	0.026393
17	-0.117958	-0.9061	0.184297
18	0.058703	0.4509	0.326854

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

R code (references can be found in the software module):

if (par1 == 'Default') {
par1 = 10*log10(length(x))
} else {
par1 <- as.numeric(par1)
}
par2 <- as.numeric(par2)
par3 <- as.numeric(par3)
par4 <- as.numeric(par4)
par5 <- as.numeric(par5)
if (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'
par7 <- as.numeric(par7)
if (par8 != '') par8 <- as.numeric(par8)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
dev.off()
(myacf <- c(racf$acf))
(mypacf <- c(rpacf$acf))
lengthx <- length(x)
sqrtn <- sqrt(lengthx)
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Autocorrelation Function',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Time lag k',header=TRUE)
a<-table.element(a,hyperlink('basics.htm','ACF(k)','click here for more information about the Autocorrelation Function'),header=TRUE)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,'P-value',header=TRUE)
a<-table.row.end(a)
for (i in 2:(par1+1)) {
a<-table.row.start(a)
a<-table.element(a,i-1,header=TRUE)
a<-table.element(a,round(myacf[i],6))
mytstat <- myacf[i]*sqrtn
a<-table.element(a,round(mytstat,4))
a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Partial Autocorrelation Function',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Time lag k',header=TRUE)
a<-table.element(a,hyperlink('basics.htm','PACF(k)','click here for more information about the Partial Autocorrelation Function'),header=TRUE)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,'P-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:par1) {
a<-table.row.start(a)
a<-table.element(a,i,header=TRUE)
a<-table.element(a,round(mypacf[i],6))
mytstat <- mypacf[i]*sqrtn
a<-table.element(a,round(mytstat,4))
a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code